What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)+12y=0 ?

The solution for (d^2y)/(dx^2)+8(dy)/(dx)+12y=0 is y=c_{1}e^{-2x}+c_{2}e^{-6x}

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(d^2y)/(dx^2)+8(dy)/(dx)+12y=0

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0

y = c_{1} e^{- 2 x} + c_{2} e^{- 6 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 6 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 6 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 37 y = 0

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0, x (0) = 3, x^{^{'}} (0) = 14

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 6

y^{^{''}} + 128 y = 0

x^{^{''}} = r^{2} x

What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)+12y=0 ?
The solution for (d^2y)/(dx^2)+8(dy)/(dx)+12y=0 is y=c_{1}e^{-2x}+c_{2}e^{-6x}